Electron beam oscillator



Jan.13,1942. WHANSEN ETAL 2,269,456

ELECTRON BEM OSCILLATOR WML/AM WHA/MEN RUSSEL/.H AH/ /v Jan. 13, 194,2.

w. w. HANSEN Erm.

ELECTRON BEAM OSGILLATOR Filed Jan. 22, 1938 6 Sheets-Sheet 2 I 'r` .1 L 90 I 7 4 '.VeZoczzf`1/= V I 1 Jan. 13, 1942. w, w, HANSEN ETAL i 2,269,456

ELEGTRON I BEAM OSICILLATOR 1 Filed Jan. 22, 1958 6 sheets-shet' 5 INVENTORS WML/AM m AA/55N j? #assai/L .mfr A/v ATTORNEY Jan.13,1942'. W,W,HANSEN ETAL 2,269,456

ELECTRON BEAM OSC ILLATOR Filed Jan. 22, 1958 6 sheets-sheet 4 BY RUSSELL j ATOZY. l L* Jan. 13, 1942. w. iw. HANSEN ETAL ELEGTRQN BEAM OSCILLATOR Filed Jan. 22, 1958 6 Sheets-Sheet 5 INVENTORS WILL/AM M/.HA/VJEN HUsELLH. AR/A/v B2i/0M ATTORN Y.

m1211242. W.W.HANSEN' mL 2,269,456

' f ELECTRON BEAM oscILLAToR INI/ENTORJ RUSSELL/Ll, VAR/,AN

meme am.;v 13, 194e n' ELECTRONBEAM OSCILLATOR William W. Hansen and `Russell H. Varian, Stanford University, Calif., `assignorg to Board of Trustees ot the Leland Stanford Junior University, Stanford Universlty, Calif., a corporation o! California Applicationv January 22, 1938, Serial No. 186,316

, I31 Claims.

The presefnt invention relates, generally, to electrical converters or oscillators, and the invention more particularly is concerned with thev conversion of the energy of a unidirectional current into the energy'oi an alternating electromagnetic eld. JIts iield of application is principally in the region of frequencies of lliI cycles per second and higher. It is related to the earlier inventions disclosed in copending applications: Ser. No. 92,787, filed July 27, 1936, for High emciency resonant circuit, W. W. Hansen, Patent No. 2,190,712, and Ser. No. 168,355,

. illed October ll, 1937, for Electrical converter,

R. H. Varain, now Patent No..2,242,275.

In Patent No. 2,190,712 for High elciency resonant circuit, there is described a resonant circuit characterized by an electromagnetic field bounded by the conducting surfaces of a substantially closed non-radiating container. In

' this circuit'the contained iield appears as sustained standing waves. .This is vdisclosed also in-subsequent copending applications: Ser. No. 185,382, filed January 17, 1938, for Radio measurement of distances and velocities," W. W. Hansen and R. H. Varian, Ser. No. 193,268, filed vMarch 1, 1938, Electrical converter, W. W.

Hansen, R. H. Varian, and L. M. Applegate, and` Ser. No. 201,898, flled April 14, 1938, Radio transmission and reception, W. W. Hansen and R. H. Varian.

In Patent No. 2,242 ,275, it is shown howto produce oscillations using an electron beam projected through two space-resonant devices of the above-described character, the combination being referred to as a "klystron. A klystron, in preierred form, is an` electrical converter and/or Another object of the present invention lies in the provision of a novel electrical converterI of the above character employing a single enclosed resonant circuit through which a beam of electrons is adapted to be directed to establish a standing electromagnetic ileld therein, the electrons moving preferably parallel to the electric vector of the field, which vector preferably varies in intensity throughout the length of the circuit to effect highly eiiicient operation, the dimension oi' said circuit along the axis of said beam being such as to enable speeded up electrons to overtake slowed down electrons and hence produce groups which are allowed to leave the circuit at lowered velocities, thereby giving up energy to the resonant circuit field and maintaining the same in oscillation. .y

Still another object of the present invention is to provide a novel electrical converter of the above character having such physical coniiguration as to enable the maximum possible absorpv tion of energy from the electron stream for maintaining the converter in operation and -for supplying any desired load.

^ parent from the specification, taken in connec- Other objects and advantages will become aption with the accompanying drawings wherein the invention is embodied in concrete form.

amplier composed of two or more space-resonant devices excited and coupled by a beam of i electrons projected through the electromagnetic fields contained in the space-resonant devices. We have also referred to the first space-resonant device in a klystron as a buncher and the second as a catchen In the buncher, the electrons are alternately accelerated and decelerated at the frequency of oscillation of the field of the buncher, and in the catcher, the

energy ofthe bunched electron beam is converted into electromagnetic-field energy. We shall usey these terms in our present disclosure.

'I'he principal object 'of the present invention is to provide a novel electrical converter employing a single space-resonant device and serving as an efficient generator of ultra-high-frequency alternating currents and being capable of delivering large power.

In the drawings:

Fig. 1A is a diagrammatic representationoi a "klystron. V l

Fig. 1B is a graph of certain electric elds relating to Figure 1A.

Fig. 2A is a diagrammatic representation oi .our present invention 'in a form suitable for purposes or explanation..

Fig. 2B is a graph of certain electric iields relating to Figure 2A.

Fig'. 3A is a graph of electron velocities plotted l with time (t) as abscissa relating to Figure' 1A. Fig. 3B is a graph of electron velocities plotted with time (t) as abscissa relating to Figure 2A. Fig. 3C is a graph of electron velocities plotted .with distance (z) as abscissa relating to vFigure 1A.

Fig. 3D is a graph oi electron velocities plotted with distance (z) as abscissa relating to Fig-l Fig. 3E is a graph ot distances traversed by certain electrons plotted withtime (t) as ab scissa relating to Figure 1A.

Fig. 3F is a graph of distances traversed by certain demons plotted with time (t) as abscissa relating to Figure 2A.

Fig.,4 is a curve showing voltage and current,

necessary to start oscillation.

Fig. i5 shows a present preferred form of embodiment of our present invention.

Figs. 6A, 6B, 6C and 6D are alternative forms of our invention.

Figs. 7A, 7B and 7C forms.

Fig. 8 shows another form of the invention.

A distinction between thev klystron" and the present invention is that in the klystron at least two separate electromagnetic fields are employed, one for bunching an electron beam, that is, for changing the electron velocities, and one for catching," that is,taking energy from the beam; while in the present invention we use asingle electromagnetic field for buncher and catcher and the space in between. Because of this characteristic, we call our present invention the lare I other alternative monotron, that is, a single thing. The name is properly used as a noun modifier such as in the expressions monotron oscillator, monotron detector, et cetera. In the klystron oscillator, the two space-resonant devices are bilaterally coupled together by inductive loops or other means. In the -monotron, only one spaceresonant device is required, inasmuch as only one electromagnetic field is used. This arrangement is of course simpler than the earlier one,

that of lthe klystron, but in some ways it is not so flexible. In general the modes of `application and uses of the klystron are applicable to the montoron.

The monotron is very simple in its physical embodiment, as will be shown, but the mathematical considerations underlying its invention and reduction to practice are comparatively complex. Accordingly, in the present disclosure we will set forth the principal mathematical relationships involved in order that those skilled in this phase of the art may have a basis upon which to conduct theoretical investigation of our invention. However, a disclosure sufficient for the practical use of our invention would not require more than a few diagrams and a simple explanation.

As the preliminary part of the mathematical description of our present invention, we will review some of the theory of the klystron. For this we begin with Figure 1A, which shows a klystron oscillator in which I is an emitter of electrons, 2 an accelerating battery, 3 a spaceresonant device with a pair of spaced grids 4 and 5, 6 a second space-resonant device with a grid 'I and a grid or plate 8 spaced therefrom, 9 and II are coupling loops connected by a pair of conductors I2, preferably in the form of a concentric line, and I3 is a coupling loop for output. Briefly, the operation is as follows: A beam I' of electrons is projected from the emitter I through the grids 4/and 5 where positive and negative accelerations of electrons in the beam occur alternately at the natural frequency of the system. The electrons leaving grid 5 travel toward grid 'I at differing velocities so some electrons gain on others with the result that at grid 1 the electrons arrive in more or less clearly defined surges, or groups or bunches, in which individual electrons have velocities varying over a considerable range. Entering the field between grids 1 and 8 the bunches of`electrons periodically deliver pulses of energy to the electromagnetic field in the space-resonant device 6 at its natural frequency, thus exciting and-maintaining it in a state of oscillation.v Energy for bunching is transferred from the catcher space-I resonant device 6 to the buncher 3 by the coupling loops 9 and Il and line I2. The oscillations are started by small departures from uniformity in velocity or density of the electrons of the beam such as might be accounted for by the shot effect in the electron beam. Energy is adapted to be taken for load purposes from the catcher space-resonant device 5 by the coupling loop I3 or ,equivalent means, such as capacitive elements.

We will not proceed with the mathematical review of the klystron. Let electrons of velocity vo from the emitter I enter the field between grids 4 and 5. This field is an alternating one and is such that the value of the integral of E from grid 4 to grid 5 is Vi/'yI sin wt, where V1 is the maximum cyclic value of the voltage between grids 1 and 8, 'y is the ratio of the maximum cyclic value of the voltage between grids 1 and 8 `to the maximum cyclic value of the voltage `between grids 4 and 5, Vi/'y is the steady state maximum value of voltage lbetween grids 4 and 5, w is then 21rf where f is the frequency in cycles per second, and t is time in seconds. Let it be assumed that V1// is much less than Vo where Vo is the voltage of the electrons, that is, substantially the voltage V of the battery 2. The electron velocity vu is that corresponding to the acceleration voltage Vo. The distance between grids 4 and.5 is made, for ease in explanation, small compared with the distance traversed by an electron of velocity vo in one half cycle. An electron with velocity vo that traverses the field between grids 4 and 5 falls through a voltage Vf/y sin wt so that its velocity is changed, say to 12u-H11 sin wt. Note that sin wt is negative half the time of a period.

To Iexamine the bunching process, consider an electron arriving at grid 1 at a time t". Say that it left the grid 5 at time t; then the following relation applies:

I)0+v1 Sin (vt/ g where l is the distance from grid 5 to grid 1. Differentiating, we find that if a uniform stream of No electrons per second leaves grid 5 the density after traversing a distance l will be Now we seek to express this a Fourier series, knowing that if we succeed, the power put into the circuit associated with the grids 1 and 8 can be computed in terms of the voltage across the grids 'l and 8 and the value of the appropriate Fourierv coeficient in the series for the curand bn is a phase shift, and We inquire as to the It is advantageous to -do the integration in terms of t rather than t" so we change the variab lected vto make the constants on the rightv add to zero.V This is physically reasonable since the phase shiftb must be determined'b'y the transit time l/vn. Then wt' +b=9 t'jk sin ot' and dt"=dt'(1-k cos wt').

`flnd how much power is transferred to the circuit connected to grids 1 and 8. Suppose the voltage between grids 1 and 8 is kept .at a value just sufficient to stop the slowest electrons, that is, Vo-Vi/y. Since we have already made Vi/'y very small compared with Vo, let us simplify the formulae by taking the voltage across grids 1 and 8 to be Vo. Then the power into the catcher circuit 6 is just -VoIJi(1c). This assumes that the second circuit is running at the fundamental frequency. If it were on the nth harmonic J1(k) would be replaced by Jamie). Since the power expended in accelerating the electrons is VnI the eiliciency is J1(k). When it is possible the arrangement is designed or adjusted so 7c will give the maximum efficiency. The best value of 1c is found from tables to be 1.84 and the correspond-v ing value of Ji is 0.582. We have referred to the deceleration of electrons in the catching field as y if the action were complete, but a full understanding of the mathematics will indicate that deceleration of all electrons is not practically accomplished. Actually even under supposed optimum adjustments there may be a few electrons accelerated in the catching ileld, although most of them will be decelerated'as is desired.

The above calculations can valso be used to determine the mutual conductance `of the klystron used as an amplier. Thus, supposing k is much less than 1.84, we can approximate Ji(k) as Ic/2 and so find for the ratio of irst harmonic electron currents to buncher voltage lI/pAVo with =vnc. This increases indefinitely with l, apparently, but actually an effect due to electron space charge which we call debunching occurs which prevents utilizing very large values of l. This effect which is the result of mutual repulsion of the electrons when crowded together in the beam tends to limit the sharpness and density of the bunches as the distance traversed increases. However, with moderate values of l useful values of mutual conductance can be attained.

Finally, as to the klystron. we may note that there are three independent parameters adjustable in operation and two that are determined in the design. The rst three are: (1) the initial velocity vo of the electrons; (2) the number per second No of the electrons; and (3) the ratio y ofthe voltage between grids 1 and 8 to the voltage between grids 4 and i! The two design parameters are: (1) 4the bunching distance l; and (2) the effective shunt impedance of the catcher space-resonant device. i. e., the quotient obtained by dividing the alternating lcurrent voltage generated within the catcher-resonator 6 between grids I and 8 thereof, by the alternating current component of the electron stream current passing through this resonator. The latter parameter is often made variable, but it simplifies matters and sacrifices no essential generality to consider it 'xed.

We will not proceed to the description of the monotron, one form of which is shown in Fig. 2A, in which 2l is an emitter of electrons, 22- an accelerating potential battery, and 23 an evacu-v ated shell constituting a space-resonant device of special shape. The shell 23 has a bounding surface including apertured grids 24 and 2l in oppositely disposed end faces of the space-resonant device 23. By comparison with the klystron of Fig. 1A, it will be seen that the two spaceresonant devices 3 and 3 and the associated cou" pling loops 9 and Il have been replaced by a single internally resonant conducting hollow body 23 in Fig. 2A. The electron stream from the emitter 2| has a substantially uniform distribution in time outside the resonator 23. In operation, the space-resonant device 23 contains a confined resonant oscillating electromagnetic ileld with a substantial magnetic field component and having standing waves. The electric eld component extends along the axis of device 23, i. e., from the center of grid 24 to the center lvof grid 25, and its magnitude is E(z) cos wt with E as represented in Fig. 2B, in which E is'the electric eld strength within container 23 along the axis of the electric eld component and also .along the axis of lthe electron beam projected through member 23, :n .being the distance from grid 24 toward grid 25. The cavity resonator 23 may also be constructed so as to support a direct current field, but this possibility will be neglected for the moment. As will develop pres-L ently, the exact shape ofthe curve for E(z) along the path of the beam'is unimportant-all we need to know when carrying out asample calculation is that it has no discontinuities, i. e. sudden changes in the value of the electric field component and this is true as long as .there are no conductors on the axis inside the space-resonant device. 'Actually the device will operate with discontinuities in the electric Vfield vector, such as those caused by conductors, but such forms of the invention require more complicated A.

calculations which will not be given here. distinction between the arrangement shown in ilrst the ratio of the voltage drops in the electric vector extending` between the grids 4 and l and between grids 1 and 3 was adjustable while in the second a corresponding ratio exists in the field strengths adjacent the grids 24 and 25, but

'in the case of Fig. 2A this ratio is determined by the design. Thus the three` adjustable parameters, i. e accelerating voltage, back-coupling and current, in the klystron are reduced to two.

i. e. accelerating voltage and current, in thel 'monotron and the number dependent upon the,

design are increased by one in the monotron.

Thus, the simplication of design sacrifices the adjustability of one parameter.

'In the monotron, as in thev klystron, a beam v interspace between the grids 1 and 8.

in the actions oftwo representative electrons of the beam are traced in their motion through the klystron or monotron, as the case may be. These two electrons will afford a picture of what happens to the remaining electrons of the beam. In Fig. 3E, corresponding to the operation of the klystron structure of Fig. 1A, one electron is represented by a solid line while the other is represented by a dotted line, these lines having the same slope, as indicated at 90 and 9|, respectively, during that portion of the travel of the electrons before they enter the space between grids 4 and 5, being th'us indicative of the fact that both electrons have the same velocityy dur-J ing this initial period. The electron represented by the dotted line 90, leaving cathode earlier, reaches the interspace between grids 4 and 5 first, and assuming that the instantaneous electric field in the interspace opposes this electron, its movementwill be retarded, as represented by the dotted line 92. The electron represented by the solid line 9| reaches the interspace a After aids its motion, and hence increases in velocityV as shown by the upward slope of this solid line 9|. This electron, represented by the full line 9|, although leaving the interspace 4-5 later than the electron represented by the dotted line 90, nevertheless overtakes the latter at the time it reaches the interspace between the grids 1 and 8. Both electrons, after traveling between the grids -5 and 1, as represented at 92 and 93, respectively, receive substantially a reduction in velocity in passing through the opposing field extending between the grids 1 and 8, which may be very large relative to the changesin velocity the speeded-up electron represented by the solid line 93 has overtaken at 95 the slowed-up electron, represented by the dotted line 92. The portions of the paths of these electrons between the grids 4 and 5 are omitted for purposes of simplification. l

These two electrons are representative of a group that is thus formed upon entering the Within this interspace the group or bunch of electrons is adapted to be subjected to an alternating elec- 1 and 8, but at this time there are fewer electrons passing between these grids since this portion of the electron beam has been rarefled due to the bunching operation, with the result that the field does not lose as much energy to these fewer electrons as it gained from the relatively greater number of hunched electrons passing through during the previous half cycle, and hence, because of the net energy supplied to them, the oscillations in resonant circuit member of Fig. 1A will tend to increase in amplitude. Consequently, all that is required initially is a very small transient oscillation, no matter how initiated, in the right phase in member 6 and it will grow to largevalue when thus supplied with energy from the bunched electrons. The proper coupling, provided by line I2 and loops 9 and between circuit members 3 and 6 serves to cause the beam to be bunched when it reaches member 6, whereby alternating current energy may be extracted therefrom. Thus, the device of Fig.

lA becomes a self-excited oscillator.

caused by the bunching operation; This is but another `way of stating that a large proportion of the original energy given to the electrons by the accelerating field of the energy source comprising the battery 2 may be transferred to the oscillatory field in the catcher resonator 6.

In Fig. 3F, corresponding to the operation of the monotron structure of Fig. 2A, it will at present be assumed for purposes of explanation that the alternating electric field extending between the grids 24 and 25 is uniform in space.

Then, if the electron represented by the dotted line 96 enters the space between the grids 24 and 25 with velocity vo at a time when the field within this space is zero and about to increase y in a direction to oppose'the motion of the elecill tron, the latter, in its further travel in the field, will be slowed down for the first half-cycle of oscillation of the field, as represented at 91, and will be speeded up, as indicated at 98, in its passage during the second half-cycle, so that at the end, of the full cycle, it will have the same velocity at 99 as that with which it entered the space. During the remainder of the time that this electron is in the interspace between the grids 24 and 25, its velocity will be decreased due to the reversal of field so that by the time it leaves the grid 25 its velocity is below that at which it entered the grid 24. Since this electron was initially slowed down upon its entry into the field of resonator 23, its average velocity therein is below that which it possessed at its time of entry, i. e. below vo.

Similar reasoning will show that the electron represented by the solid line |00 entering later and at the beginning of the reverse half-cycle will have an average velocity within the space between the grids 24 and 25 that is greater than vu, as represented at l|0|. Thus, it will be clear that electrons with higher than average velocity following electrons with less than average ve- `locity will overtake the latter at 94 and form an electron bunch or group similar to the bunch or group found in the klystron upon entering the space between the grids 1 and 8 thereof. If, now, this group leaves the electric field through the grid 25 at a time when all the electrons in the bunch have minimum velocities, the fastest electrons of the group will have a velocity of about vo, assuming the electric vector to be of uniform strength for all values of X, whereas the slowest electrons will have a velocity considerably less than this. Though the electrons have both gained energy from and lost energy to the field during their travel therethrough, therefore, the group as a whole, by the time that the electrons have left the field, has delivered energy to this electromagnetic field between the grids'24 and 25. Assuming the energy lost by the electrons as a whole to the field is great enough to I maintain the field, that is to supply all losses, and thus to effect bunching of the electrons, the device will act as a self-oscillator.V

If desired, the proportions of the resonator 23 and the frequency of the oscillation may be made such that the electron remains for a longer period within the resonator, but the net result will be the same so long as the electrons leave the resonator at reduced velocities. In this event, the second and subsequent cycles will be a repetition of the changes brought about during the first cycle.

In the device of Figs. 2A and 2B, the electric field increases in strength progressively along the axis from the grid 24 toward the grid 25, as described hereinafter in connection with Fig. 6C. v The dotted-line electron that loses energy inthe first half-cycle, therefore, doesnot always have its initial energy or less, as in the case just considered. This will be understood from the description hereinafter of Fig. 3B. Nevertheless, it is still true that the electrons that have been slowed down in their rst halfcycle in the interspace between the grids 24 and 25, will have less average velocity throughout the remainder of their passage through this space than those that are speeded up in their iirst half-cycle, and so bunching of course occurs, and with the bunches passing through the' grid 25 when they have minimum velocity, they will deliver energy to the field existing between the grids. l

Ii; will be recalled that in the initial discussion in which the electric field wasv considered uniform between the grids 24 and 25, the faster electrons, in passing out of the field through the grid 25, delivered only the energy they had received in the rst half-cycle after they entered through the grid 24, and hence these electrons contributed nothing to the-energy of the field.

If, however, as shown in Fig. 6C, the field increases in strength between the grid 24 and the grid 25, which is true of the structure shown in u Fig. 2A, as hereinafter explained, energy may be extracted from both the fast as well as the slow electrons, for all electrons of the bunch stead of the velocity being plotted as a function of time for the electrons in their travel through the oscillator, the velocity is plotted as a function of distance. The dotted 'line 90 represents an electron that, when entering the space-resonant device 3 at the grid 4 at a certain time, is decelerated. The solid line 9i represents an electron that, when entering the space-resonant devicev 3 at the grid 4 a half-cycle later, is accelerated. Because the electron represented by the solid line 93 has a higher velocity in the space between the grids and 'l than the electron represented bv the dotted line 92. it may reach the grid 1 at the same time as the electron represented by this dotted Vline 92. If this is the case, both electrnns will suffer approximately. the same 4loss in velocity. as represented in Fig. 3C by the sharp drop in both the lines between 1 and 8.

Figs. 3B and 3D have the same significance for the monotron as has been previously stated in connection with Figs. 3A and 3C for the k1ystron. In Fig. 3B, the earlier entering, dot ted-line electron enters through the grid A24 at 'a 'time when the iield'inthe resonator 23 is zero and about to oppose the motion of the electron." In the subsequent half-cycle ojf the resonator 23, therefore, the electron represented by the dotted line is decelerated. In the next halfcycle, the electron is accelerated again and, since the field is increasing in strength from the gridv 24 to the grid 25, it will reach a velocity slightly greater than its initial velocity, as shown in Fig. 3B, when it reaches the point 80. Its velocity will then decrease again, reaching a new low velocity at 81, from which the velocity will increase and reach\ another high at 82. vThis will continue until the electron leaves the iield at the grid 25.

Anelectron entering the field one-half cycle later will be accelerated during its first halfcycle in the eld and will reach a velocity maximum at the time, corresponding to that of 80. It will then lose velocity, vreaching a velocity 'minimum at the time corresponding to the point 81. It will then gain velocity, so as to attain a velocity maximum at the time ,corresponding to the point 82, and will continue, in a similar manner, until it leaves the grid 25 with reduced velocity, as did the dotted-line electron represented in this Fig. 3B.

' ing to Fig. 3C for the klystron, the velocities of the electron being lplotted as a function of distance. In this case, an electron represented by the dotted line enters through the grid 24 at a time when the field in the monotron is zero and changing in a direction to oppose the motion of the electron. This electron is rst slowed down for a half-cycle, so as to reach` a `minimum velocity at a distance indicated by the point 83. From this point, the electron velocity is increased to a new maximum 84, that is shown somewhat above the `initial velocity. In the cycle between the entrance of the electron at the grid 24v and its arrival at the point 84, the average Velocity of the electron has been below its initial velocity. This electron then goes through another cycle of velocity changes between the points 84 and 86, through a minimum 85. In this second cycle, the average velocity of the electron is also below the initial velocity. The electron continues in the same manner until it reaches the grid 25, where it leaves the field of the resonator 23 withv reduced velocity.

The solid line of Fig. 3D represents an electron that enters the eld one-half cycle later than the electronrepresentedby the dotted line, receiving consequently an initial acceleration from the eldfand reaching its rst maximum velocity at 87. It then loses velocity, reaching a minimum velocity at 88. In this cycle spent in the resonator 23, the average velocity of the electron was above the velocity with which it entered through the grid 24. Since this electron has traveled faster than the electron represented by the dotted line of this Fig. 3D, the distance along the, axis separating the successive maxima and minima of velocity is greater than it was by the electron represented by the dotted line. The pointi88, representing the minimum velocity of the electron, therefore, is somewhat farther along the :n axis than the .point 84, representing the maximum velocity of ,the electron represented by the dotted line of this Fig. 3D. If this electron is followed through the' succeeding cycles of its passage through the resonator 23.

it will be found that, throughout its passage, it maintains a higher average velocity than the electron represented by the dotted line. 'Ihe points represented by successive maxima and minima on this curve will progressively get farther and farther ahead of the corresponding points of the dotted-line curve until, when the electron reaches the region immediately in front of the grid 25, it willhave gained one-half cycle on the electron represented by the dotted-line curve, and will suffer-a large loss of velocity `during the half-cycle just before passing through the grid 25, the same as was the case with the electron represented by the dotted-line curve which entered through the grid 24 one-half cycle earlier.

As shown in Fig.4 3D, the distance the electrons have traveled is such that the electron represented by the dotted line and that represented by the solid line arrive'at the grid 25 approximately at the same instant, at a time when their respective velocities are both at a minimum. They will therefore have delivered energy to the alternating eld in the resonator 23 it is possible, however, by slightly changing the velocities of the electrons in their transit y from the grid 24 to the grid 25, to cause the electrons represented by the full-line curve and the dotted-line curve to arrive together at the grid 25 at a time when they Will have a maximum, instead of a minimum, velocity. Under these conditions, the electrons .of the electron stream will absorb energy from the resonator circuit, instead of delivering energy to it, so that any initial transient oscillations would die out instead of being built up into steady-state oscillations. AThis change of velocity may be effected bya `change of voltage applied between the cathode 2i and the grid 24. By maintaining the field of resonator 23 from some external source the electrons may thus be speeded up.

In the monotron, however, the oscillating electric field contained in the resonator 23 has a component at substantially all points of the field in substantially the direction of travel of the electron stream at certain times and in substantially the opposite direction at other times, during alternate half-cycles. through the resonator 23, the electrons interact with the field of the resonator at the resonant frequency of the field, so that their speed, in the direction of travel thereof, becomes increased and decreased, and the electrons become thus concentrated in groups in a -region of the eld prior to reaching the grid 25. Such interaction may be produced by, for example, regulating the time of flight of the stream in the eld. The field of the resonator is less intense at its boundary adjacent to the grid 24 than at its boundary adjacent to the grid 25. Increments and decrements of energy of the period of the field are imparted to the electrons both near the grid 24, to cause the electrons to assume periodically varying velocities, and in a subsequent region of the field, vbut the increments and decrements imparted individually to the electrons in the subsequent region are greater than those imparted to the electrons at the grid 24, with the decrements exceeding the increments. The energy of the groups becomes ultimately absorbed by, or delivered to, the field at the resonant frequency of the field just before the electrons arrive at the grid 25. The electrons thus leave the field of the resonator 23 with less energy than they had when they en- During .their travel tered it and electromagnetic resonance is excited and maintained in the field at the resonant frequency of the field to sustain oscillations in the field.

The space-resonant device 23 is of such proportions and the electrons of the stream have such velocities as to establish the before described electromagnetic field therein. Specifically, the dimension of the space-resonant device 23 in the direction of travel of the electron stream and the resonant frequency of the field are so related to the velocity of the electron stream in the space-resonant device- 23 as to cause the field to abstract energy from the electron stream.

The portion of the field of the space-resonator device 23 immediately adjacent to the discontinuity or breaking off of the field at the grid 24 and due to the presence thereof performs the same function that the eld between the grids 4 and 5 does in the klystron, and the portion of the field between the inside and the outside of the space-resonant device 23 'at the discontinuity immediately adjacent to the grid 25 performs the same function as the field between grids 'I and 8 in the klystron. Of course,

the field need not be strictly discontinuous. All

that is required is that the field change greatlyv in a space short compared to the distance traversed by an electron in, say, one cycle. Such a discontinuity is easily produced at a properly designed grid. On the other hand, what is practically a mathematical discontinuity in the eld occurs at the conducting surfaces. In the space inside the rhumbatron the field may be of high intensity, whereas inside the conductor at the boundary of the field the intensity is nearly zero. Thus, a discontinuity in field might occur at a grid, or at a conducting surface, and this latter might be a surface where electrons arrive or it might equally well be a surface from which they are emitted. The similarity in the principles of operation will be apparent from the mathematical considerations to be presented.

If an electron of charge -e, enters the rst grid 24 at time t=t0, with initial velocity vo determined by battery 22, Qits velocity at any later time t will be 1 where E is the value of E(:c) where the electron is at time t'.

Here we could add also a term toA account for a unidirectional field that might be superimposed on the oscillating field. For convenience this will be omitted, but it will be apparent from a full understanding of the theory that a unidirectional field should be provided for. The essential parts of our invention are a unidirectional field, an oscillating field and a stream of electrons in the oscillating field. Also, as indicated, the oscillating field must have what amounts to separate field portions adjacent to the two grids 24 and 25 before-mentioned forrespectively changing the velocity of the electrons to enable them to become grouped and to absorb the energy of the groups. When the adjustments are right, the electrons can effect transfer of energy from the unidirectional field to the oscillating field., In Fig. 2A, the unidirectional and oscillating fields are shown separate, the unidirectional iield being between the cathode 2l andthe grid 24, outside the oscillating field, while the oscillating field is confined in the enclosed space between the grids 24 and 25. In Fig. 5, the fields are shown partly superimenough, by repeated integration posed, the unidirectional iield produced by batteries 2i and 35 being between the cathode 26 `and the Igrid 32. In Fig. 8, these fields are com- Averaging v over the transit time-through the space-resonant device 23, which usually covers several cycles, the terms due' to the upper limits practically'drop out. The series of lower-limit terms usually converges rapidlyrand in the few cases where it does not, the mairisresults are substantially the same, so we shall` drop all terms after the The average speed of the electron is therefore mme-E@ sin wt ma! l vHere E(0) is the peak oscillating field intensity at the entrance grid 2d. Thus the average velocity of the electrons depends only on their time of entrance and on the magnitude of the discontinuityin field at =0, as represented in Fig. 2B. Note that a superimposed unidirectional eld would not greatly lchange the'diflerence in velocity between the fast and slow electrons which is responsible for the bunching process. Therefore the bunching will occur in muchl the same way in the apparatus of Figure 2A as in that of Figure 1A and the fact that the electron velocity oscillates during the bunching instead of remaining constant as in Figure 1A. has no great eiect.

Referring again to Figure 3D, it will be seen vthat if grid 25 is moved back toward the origin it will be encountered by the bunched electrons when they have maximum velocity instead of minimum velocity. Under this condition they would take energy away from the field in the space-resonant device 23 and would tend to stop by parts. Thus grids 24 and 25, and is a continuous function of z, i. e., the distance towardgrid 2 5 from grid 24, but drops substantially discontinuously to zero at these two grids, as is shown in Fig. 2B.

Through the grids passes a prescribed stream of electrons going at a velocity determined by the voltage of the battery 22. We intend to compute how much alternating current power is delivered to the rhumbatron 23 and what fraction this is of the direct current power supplied to the electron beam. In performing the calculation` we will consider as known any needed characteristic.

of the rhumbatron or yoi the eld produced by it.

To perform the calculation, we proceed as foilows. We take the change in average velocity of the electrons from Equation 7 and insert into Equation 4 getting for the peak value of the first harmonic component of current at the secondl grid I6J`1(k)where Io is the direct current and Ic=E(O)/2V, where V is the accelerating voltage of battery 22. Likewise, the second harmonic is r Io2J2(2K) and it will be found that higher terms 'depend on the electron velocity, and on E(l) and p is found by using (7). to be oscillation. This is the condition for accelerating a stream of electrons in a rhumbatron driven by another electron beam or by an outside oscillator. l

or by changing the field in the space between the -cathode 2i and the grid 2G. This acts on all the electrons alike and changes their transit time without greatly changing their nal velocity. The way this ileld is applied is shown in Figure 5. In the mathematical discussion we will assume that the dimensions of the system are as presupposedv in Figs. 3BA and 3D. l

Thestructure of Fig. 2A, consisting of the en i closed `'resox'iant circuit having entrance and exit grids 2,4,k and 25, will serve as a self-oscillator if,

.as is-well known, at a very small amplitude of oscillation the device manages to extract more energy in oscillatory forml from the electron streagthan is necessary to' maintain the small I oscillation we have assumed to exist. That this l can be the case in this devicel is 'about to be.,

showfglf` The oscillatory field is set 'up between Physically this corresponds to the requirement4 that the electron shall not lose more velocity than it has, that is, it mustnot be turned back. Of course, the apparatus can be run so that some electrons are turned back but for that case these computations do not apply. Also, it has been assumed that the change in average velocity is small compared to that velocity. The apparatus can run well even though this assumption is not fullled.

Now we can compute the total power put into the eld by using (8), and the Fourier series for the current, and remembering that not all electrons deliver the maximum energy to the eld. On the other hand we will assume that the average transit time is such as to make the electrons deliver as much energy as possible. This condition may be met in practice by adjusting the electron voltage or by adjusting various direct current elds in the rhumbatron or by concurrent adjustment of both. The power so computed -is to be equated to the power required tokeep the rhumbatron in oscillation. We will take this to be a'E2(1) where a' depends on the losses and loading of the rhumbatron. That is, a' is of dimensions cm.2/ohm and takes into account both the power used in the rhumbatron and the power that maybe used usefully. Thus, for any given rhumbatro'n there exists a minimum u; this may be increased by coupling in a load. We iinally find This essentially solves the problem. This is seen when we remember that E(O) and E(l) are rethe power into the rhumbatron and the eiiiciency of the conversion from a unidirectional current to the energy of an oscillating field.

This is not the preferred form for solution so a simplification is made and a scheme for calculation introduced. This is done by considering E and V as given and solving (9) for Io. The eiciency is also found in terms of E and V and so we can find values of Iu, V and efficiency that go together. Changing to morejconvenient units we nd Looking at these formulae We'see that if we plot contours of constant efficiency using I and v/a2 as variables then we can use the same chart for all monotrons, individual differences being taken into account in the factors converting I and v/a2 into actual amperes and .volts.

We may notice that, for present purposes, three quantities characteristic of the rhumbatron are of importance. v These are x=E(l) /E(O), the ratio of exit to entrance field strength, l/)\, the ight distance of the electrons measured in wave lengths, and 41r x1/x2, which is a measure of the energy required to maintain the field inside the rhumbatron.

An unnecessarily extended discussion could be based on Equations 10 and 11, and their relation to oscillator efficiency, modulation, et cetera, and with slight additions discussion could be given of regenerative, super-regenerativeand oscillating detectors, et cetera. Most of this will be reserved for the future, however, and at the moment we will only discuss some points of immediate interest.

First, we note that the line of zero efficiency bounding the region of oscillations is determined by letting e O whereupon we find that, just on the edge of oscillation lil-1 245% MI: 1 E I- Tl u 1.- 2wf7rl v and this equation is plotted in Fig. 4. Using the equivalents stated following Equation 11 this can be expressed as the magnitude of the electron current as follows:

were@ in -1 i2 e l 411 This, according to our computations, is the minimum electron current that will sustain oscillation in a system to which a given set of dimensional factors will apply. From this equation it is evident that a low value of a makes it easy to startoscillation, though, as we will see in a moment, it may not make it easy to get high efficiency.

We may also write down the conditions for maximum efficiency. These are found to -be MGF These combine to give where That is, the most efficient voltage is determined by l/A and y. From this we see that in order for the device to run efficiently at a reasonable voltage lk l cannot be too small.

The current that goes with maximum efficiency is easily found to be and the energy that may be extracted from the electron beam in a single transit through the Vresonator 23, as above explained, may be 49 perand, if O p 1 the sines may be replaced by cosines throughout. This may be found in Bromwich, Theory of Infinite Series, paragraph 174.

Figure 5 shows the present preferred form ofy embodiment of our invention. In Figure 5 there is an emitter 26 from which is accelerated a stream of electrons by the voltage of a battery 2|. The electrons enter an evacuated portion 16 of the shell 28 and an evacuated internal portion 29. At the entrance of shell 28 there is a grid 3| corresponding to grid 24 in Fig, 2A.l The surface 32 which may be either solid or perforated corresponds to the grid 25 in Fig. 2A. Depending upon the relative proportions of the spherical surfaces 28 and 29 shown in Fig. 5, a field inside may be produced that is more concentrated at the surface 32 than at grid 3 I. This, as is indicated by the computations, is desirable in order to attain high efficiency and ease of I general and it is supported on a circular conical section 33. The two sections, 28 and 29, are insulated at an annular joint 34 which has a relafield isl therefore less at the convex end 52 thanT tively high capacitance between the two sections. Across the insulation of the joint 34 there is the .battery 35 which superimposes a unidirectional electric field on the alternating field of the spaceresonant device. By adjusting the strength of the battery 35, it is possible to adjust the time o'f flight of the electrons through the evacuated chamber 16 and also to adjust the relative time spent by the electrons in the vicinity of the'grid 3| to the time spent by the/electrons in the vicinity 'of the grid 32. It is also possible to adjust the flight time of the electrons in the chamber 16 by means of the battery 2| exactly as described in connection with Fig. 2A, without any change in the relative time spent by the electrons near the grid 3| compared to that spent by the electrons near the grid 32. By independent adjustment of batteries 2l and 35,

therefore, it is possible to obtain a desired flight time, and also a desired time spent by the electrons in the vicinity of the grid 3| to that spent v by the electrons in the vicinity of the 'grid 32.'

Provision for transferring energy into or out of the system is illustrated as made with the couplingeloop 36. The system can radiate through the hole 31 when this hole is provided. The operation of the arrangement shown in Figure 5 follows the theory already presented. In series with the battery 2| there is shown a source of alternating voltage 38 which whenoperating superimposes an alternating voltage on the direct accelerating voltage for modulating pur-- poses. This alternating voltage may be used to change the adjustment indicated by Fig. 3D-

in which the bunched electrons can be caused to reach grid 32 either when at minimum velocity or maximum velocity, as before described. This is useful in super-regenerative arrangements. By this method the oscillations of the system can be alternately started and stopped. In shifting to the adjustment in which the electrons reaching grid 32 are at high velocity the oscillations are stopped quickly because energy is taken from the circuit by the electron beam. This is equivalent to a large suddenly applied load for stopping oscillation, a feature which is not available in other types of oscillators.

Alternative forms of our invention are shown in Figures 6A, 6B, 6C, 6D, 7A, '7B and 7C. Figure 6A shows the development of a right circular cylinder into a form suitable for our invention. In the diagrams lines have been .drawn to indicate qualitatively the electric lines of force. In Fig. 6A, the lines of electric force 50 of the electromagnetic eld are shown parallel to the axis of the cylinder. Thus the field may be said to be symmetrical in space. In other figures, however, the space-resonantdevice is shown nonsymmetrical about a plane between the grids 24 and 25 perpendicular to the axis of the electric field to render the electric field component of the electromagnetic eld substantially stronger at the grid 25 than at the grid 24.

Fig. 6B is derived from Fig. 6A by making the top of the cylinder convex at 52 and the bottom concave at 54, as viewed from the outside. The

resulting lines of force 56 converge from ther.

convex top 52 toward the concave bottom 54. The spacing between the lines of force 56 at a particular point is inversely proportional to the spacing between the lines of force at the convex upper end 52 is greater than the spacing between the lines of force at the concave bottom end 54. The electric field strength of the electromagnetic v'similar to the lines of force l56 of Fig. 6B. 'I'he strength of the field at the smaller end 60 is smaller than the strength of the field at the larger end 52.

Fig. 6D is derived. by combining the modifications of Figs. 6B and 6C. The corresponding lines of force 64 diverge a little more strongly than the lines of force 56 and 58. These-arrangements of Figs. 6B, 6C and 6D increase the field intensity at one end relative to the intensity at the other over what is obtained with the cylindrical arrangement of Fig. 6A. This is desirable for practical purposes although our invention will operate with a right cylindrical space-resonant device with flat ends, as in Fig. 6A. For practical operation we have computed that this form will' operate with an electron beam voltage of 100,000 if the ratio of the height of the cylinder to its diameter is about one to three. This form has the disadvantage of requiring a comparatively large electron current for operation.

-A sphere as shown in Fig. 7A can be used in our invention but it requires such high voltages and currents for operation and the efliciency is so low that it is not considered a practical form. The hemisphere show n in Figure 7B is a practical form operating with voltages at 40,000 and currents as low as about milliampere's. This is because the lines of, electric force 66 of Fig.

7B are considerably closer together at the plane boundary 68 than at the spherical boundary 'l0 This advantage is not obtained with the lines of force I2 of Fig. 7A. The sphere deformed as shown in Fig. 7C with sharp internal projection 14 gives a good field intensity but the use of a point is undesirable because of the small area presented tovv the electron beam. Rounding the Figure 8 shows an embodiment of ourl invenf I tion possessing advantages of extreme simplici- `strength of the electric field at that point. The

ty. In it an oscillating circuit is provided by two circular surfaces 4| and 42 and a conical con-v necting surface 43. where surface 4| is connected to it there is an annular insulated capacitive joint 44, across' which is applied a direct current potential difference supplied by a battery 45. The battery 45 serves the same function as the batteries 35 and 4| of Fig. 5. Attached to the inner `face of surface 4| there is an emitting surface 46l which is heated by a'iilament 41. The emitter 46 is support-V ed onV the surface 4| so there is no important difference of potential between surface 4I and stopped'at the discontinuity existing in the field where it is bounded by the surface 42. By making the joint 44 airtight the structure can be entirely self contained and evacuated.

In this surface preferably` oscillate by the methods we have described.

However, in practice, shapes will ordinarily be restricted to' those simple forms that can be conveniently manufactured and which give the desired shape to the contained electromagnetic field. The design of the forms is subject to the application of weil known electromagnetic theory augmented by the mathematical development we have presented.

The application of the' present invention to uses as an amplifier, detector, oscillator. or in other ways can be accomplished with reference to the above-mentioned patents and copending applications which show inl detail how to apply the klystron for these purposes. .In general anything that can be done with the electron beam leaving a klystron can be done with the electron beam where it leaves the second grid of the monotron. It is not to be expected that the monotron will displace the kiystron in all applications. Each has certain advantages that will be apparent to those skilled in the art. The simplicity of the monotron recommends itparticularly for applications where the flexibility of the klystron is not needed, as in some types of oscillators.

l Having described our Y invention what we claiml is:

- l. The method of exciting a resonant circuit having an enclosed electromagnetic field, which consists of causing a stream of electrons to enter a region substantially enclosed and containing the oscillating electromagnetic field of said circuit and to pass through it, causing the electrons tobe subjected to alternate increases and decreases of speed in the direction of travel thereof while in said region, and causing them to leave said region with less energy than they had when they entered it, thus sustaining' oscillation of the circuit.

2. .The method of exciting s.r resonant circuit which consists of causing a stream of electrons to enter the oscillating electromagnetic field of said circuit in a region that is substantially enclosed, causing the electrons to be subjected to alternate increases and decreases of speed in the direction of travel thereof in the field, and causing them to leave the field with less energy, in the aggregate, than they had when they entered it, thus delivering energy to the electromagnetic eld and sustaining oscillation of the circuit.

3. The method of exciting a resonant circuit which consists of causing a stream of electrons to enter a region of standing electromagnetic waves that is substantially enclosed through afield dis-y continuity at the boundary of said region, causing the electrons while in said region to interact with the field of the circuit to alternately increase and decrease the speeds of the electrons in the direction of travel thereof, and causing the electrons to leave the region through another field discontinuity with reduced energy, thus delivering energy to the electromagnetic field and sustaining the oscillation of the circuit.

. 4. The method of absorbing energy from a resonant circuit which consists of causing electrons to enter a field of standing electromagnetic waves that is substantially enclosed through a field discontinuity at the boundary thereof, causing the electrons while in said tleld to interact with the same and causing the electrons to leave the field through a'fleldl discontinuity at times I6 when their energy is greater than the initial energy.

different proportions at the places where the.

electron stream enters the field and where it leaves the field to render the field atlthe firstnamed place less intense than the field at the second-namedplace,

6. An electromagnetic oscillator comprising a section of an approximately spherical shell, a hollow conical member, a section of a smaller sphere placed inside the shell and connected with the shell by said conical member, the shell, the smaller sphere section, and conical member together forming a resonant chamber, said shell having a grid for admitting electrons into the chamber at predetermined orientation for producing therein the oscillating electromagnetic eld.

7. Apparatus of the character described comprising, cavity resonator means, means for creating `an electron stream for passage lineally through said cavity resonator means to thereby set up a standing electromagnetic field therewithin, said cavity resonator means being of predetermined variable cross-section at different points along the axis of the stream so that the electric component of said field is stronger at the point where the electron stream leaves said cavity resonator means than it is at the point of entry of the electrons thereinto.

8. A closed resonant circuit consisting of a conducting hollow substantially frusto-conical member providing a chamber, one wall of which chamber is apertured and concave toward the enclosed space, the opposite wall of which chamber is also apertured and convex toward the enclosed space, and means for directing a stream l of electrons through said chamber via said apertured walls.

9. A resonant circuit comprising a conducting shell of approximately spherical form with a reentrant part presenting an approximately spherical surface within the shell, the shell and reentrant part together forming an electrically closed boundary `for a contained electromagnetic field.

' the velocity of the electrons in the direction of travel thereof in said member by an electromagnetic field resonant in said member, whereby traveling electronl groups are formed within said member, causing said groups to be alternately accelerated and decelerated by said electromagnetic field, and thereafter quickly removing said traveling electron groups from said field when :they have been decelerated to a minimum veloc- 1l. A method of controlling an electron stream that comprises causing electrons of the stream to enter a confined oscillating electromagnetic field and thereafter to travel in the field to cause the electrons thereafter to gain energy from and lose energy to4 the field, and causing the electrons to leave the field at times when the iield has gained energy on the wholefrom the elec-y trons.

' 12. A method of controlling an electron stream that comprises establishing a.resonant electromagnetic field having boundaries of different 13. A method of controlling an electron streaml during its passage through an oscillating electro- 'magnetic field having standing electromagnetic waves contained in an internally resonant conductinghollow body that comprises causing electrons of the stream to assume periodically varying velocities in a predetermined region of the field, and causing the electrons thereafter to ltravel in the field beyond the said region to produce interaction at the resonant frequency of the field between the electrons of the stream-and the field to cause the electrons of the stream, as they pass through the field, to become concentrated in groups in a second predetermined region of the field.

14. A method of controlling an electron stream duringiits passage through an oscillating electro' magnetic field having standing electromagnetic waves contained in an internally resonant conducting hollow hdy that comprises imparting to the electrons of' the stream in a predetermined regionof the 4`ifield increments and decrements of energy of the period of the field to cause the electrons of the stream to assume periodically varying velocities, and causing the electrons thereafter to'- travel in the eld beyond the said region to produce interaction at the resonant frequency of the field between the electrons of the stream and the field to cause the electrons of the stream, as they pass through the field, to become concentrated in groups inY a second predetermined region of the field.

15. A method of controlling an electron stream during its passage through an oscillating electromagnetic field having standing electromagnetic waves contained in an internally resonant conducting hollow body that comprises imparting to the electrons of the stream in a predetermined travel in the field'beyond the said region to produce interaction at thepresonant frequency of the field between the electrons of the stream and the field to cause the electrons of the stream, as they pass through the field, to become concentrated in groups in a second predetermined region of the field.

17. A method of controlling an electron stream during its passage through an oscillating electromagnetic eld having standing electromagnetic waves contained in an internally resonant conducting hollow body that comprises passing an electron stream having a substantially uniform distribution in time from outside the bodi1 into and through the field, and regulating the time of night of the stream in the field to produce interaction at the resonant frequency of the frequency of the field.

18. A method of exciting a resonant circuit ,having an electromagnetic field in a substantially enclosed region that comprises causing a stream region of the field increments and decrements of energy of the period of the field to cause the electrons of the stream to'assume periodically varying velocities, causing the electrons thereafter to travel in the field beyond the said region to produce interaction at the resonant frequency of 4the'field between the electrons of the stream and the field to cause the electrons of the stream,

- during its passage through an oscillating. electromagnetic eld having standing. electromagnetic waves contained in an internally resonant conducting hollow body, the said hollow body containing also a substantial magnetic field component, the said method comprising causing electrons of the stream to assume periodically varying velocities in a predetermined region of the field, and causing the electrons thereafter to region, increasing and decreasing the speed of the electrons in the direction of travel'thereof during their travel in the region, and causing the electrons to leave the region with less energy than they had when they entered it, thus sustaining oscillation of the circuit.

Y, 19. Apparatus for generating alternating-current energy having, in combination, a spaceresonant device having a bounding surface, means for passing an electron stream through a portion of the bounding surface into the spaceresonant device, said device being of such proportions and the electrons of said stream having such velocities that a resonant oscillating elec-l tric field is established in the space-resonantl device'to cause the electrons to assume in a predetermined region of the field near the said portion of the bounding surface periodically varying speeds of the frequency of the field, in the direction of travel of the electrons, thereby to cause the electrons to become concentrated in groups during their further travel in the eld, and to cause the electron groups to leave the field at another portion of the bounding surface to cause the electrons of the groups to transfer energy to the field to sustain it in oscillation, and a conductor coupled to the field.

20. Apparatus of the character described having, in combination, a space-resonant device, and means for passing an electron stream into the space-resonant device to establish an oscillating resonant electromagnetic field in the space-resonant device, the dimension of the space-resonant device in the direction of travel of the electron stream and the resonant frequency of the field being so related to the velocity of the electron stream in the space-resonant device as to cause tron stream and the resonant frequency of the l field being so related to the velocity of the electron stream in the space-resonant device as to cause the electrons, when in the space-resonant device. first to assume periodically varying velocities as a function of the time of entry into the space-resonant device, secondly, to cause the faster electrons to gain upon the slower electrons to cause the electrons to become concentrated in groups within the space-resonant device, and

stream in the space-resonant device as to cause the electrons, when in the space-resonant device,

first to assume periodically varying velocities as a function of the time of entry into the spaceresonantdevice, secondly, to cause the faster electrons to gain upon the slower electrons to cause the electrons to become concentrated in groups within the space-resonant device, and thirdly. to cause the groups to leave the field with less energy than when the electrons entered the field, and means for extracting energy from the field.

23. Apparatus of the .character described having, in combination, a space-resonant device having a bounding surface, and means for passing an electron stream through a portion of the bounding surface into the space-resonant device to establish an oscillating resonantelectromagnetic field in the space-resonant device, the dimension of the space-resonant device in the direction ofl travel of th'e electron stream and the resonant frequency of the field being so related to the velocity oi the electron stream in the space-resonant device as to cause vthe electrons, when in the space-resonant device, first to assume in a predetermined region of the field near the said bounding surface periodically varying velocities having the frequency of the field as a 'function of the time of entry into the space-resonant device, secondly, to cause the fasterelectronstogain upon the slower electrons to cause the electrons to become concentrated in groups during their further travel in the field, and thirdly, to cause the groups to leave the field at another portion of thebounding surface with less energy than when the electrons entered the field,.thereby to transfer energy to the field.

24. Apparatus of the character described having, in combination, a space-resonantdevice hav-v ing an apertured wall, and means for passing an electron stream into the space-resonant device through th'e apertured wall to establish an oscillating resonant electromagnetic field in the space-resonant device, the dimension of the space-resonant device in the direction of travel of the electron stream and the resonant frequency of the field being so related to the velocity of the electron stream in the space-resonant device as to cause the electrons, when in the spaceresonant device, first ,to assume periodically varying velocities as a function of the time of entry into the space-resonant device, secondly, to cause the faster electrons to gain upon the slower electrons to cause the electrons to become concentrated in groups within the space-resonant device, andthirdly, to cause the groups to leave the field with less energy than when the electrons entered the field, thereby to transfer energy to the field.

25. Apparatus of the character described having, in combination, a space-resonant device having an apertured wall, and means for passing an electron stream into the space-resonant device to establish an oscillating resonant electromagnetic field in the space-resonant device and then out of the field through the apertured wall, the dimension of the space-resonant device in the direction of travel of the electron stream and the resonant frequency of the field being so related to the velocity of the electron stream in the space-resonant device as to cause the electrons, when in the space-resonant device, rst to assume periodically varyingl velocities as a function of the time of entry into the spaceresonant device, secondly, to cause the faster electrons to gain upon the slower electrons to cause the electrons to become concentrated in groups within the space-resonant device, and thirdly, to cause the groups to leav'e the field through the apertured wall with less energy than when the electrons entered the field, thereby to transfer energy to the field.

26. Apparatus of the character described having, in combination, a space-resonant device, means for` passing an electron stream into the space-resonant device to establish an oscillating resonant electromagnetic field in the space-resonant device, the dimension of the space-resonant device in the direction of travel of the electron stream and the resonant frequencyrof the field' being so related to the velocity of the electron stream in the space-resonant device as to cause the electrons, when in the space-resonant device, first to assume periodically varying velocities as a function of the time of entry into the spaceresonant device.' secondly, to cause .the faster electrons to gain upon the slower electrons to cause the electrons to become concentrated in groups within the space-resonant device, and thirdly, to cause the groups to leave the field with less energy than when the electrons entered the field, thereby to transfer energy to the field,

and means for superimposing a non-oscillating electric field upon the electromagnetic field in the space-resonant device.

27. Apparatus of the character described having, in combination, aspace-resonant device, means for passing an electron stream into the space-resonant device to establish an oscillating resonant electromagnetic field in the spaceresonant device, the dimension of the spaceresonant device in the direction of travel of the electron stream and the resonant frequency of the field being so related to the velocity of the electron stream in the space-resonant device as to cause the electrons, when in the spaceresonant device, first to assume periodically varying velocities as a function of the time of entry into the space-resonant device, secondly, to cause the faster electrons to gain upon the slower electrons 'to cause the electrons to become concentrated in groups within the space-resonant device, and thirdly, to cause the groups to leave the field with less energy than when the electrons entered the field, thereby to transfer energy to the field, and means for superimposing upon the electromagnetic field in the space-resonant device a field of frequency different from the frequency of the electromagnetic field.

28.A Apparatus of the character described hav,-v ing, in combination, a space-resonant device having an inner evacuated portion and a surrounding non-evacuated portion separated by a dielectric boundary, and means for passing an electron stream into and through the evacuated portion of the space-resonant device .to establish an oscillating resonant electromagnetic field in the space-resonant device, the dimension of the space-resonant device in thedirection of travel of the electron stream and the resonant fre- Iquency of the field being so related to the velocity of the electron stream in the space-resonant de' vice as to cause the electrons, when in the spaceresonant device, first to assume periodically varying velocities, secondly, -to cause the faster electrons to gain upon the slower electrons to cause the electrons to become concentrated in groups within the space-resonant device, and thirdly, to cause the groups to leave the field with less energy than when the electrons entered the field, thereby to transfer energy to the field.

29. A closed resonant circuit comprising a conducting hollow substantially 'frusto conical chamber having an apertured en d wall, and

means for directing a stream of electrons into the chamber through the apertured end wall. 30. A closedresonant circuit comprising a conducting hollow substantially truste-conical `chamber the small end wall of which is apertured, and means for directing a stream of electrons Vinto the chamber through the apertured end wall.

31. Means for converting the kinetic energy of electrons'in an electron stream into high frevquency electromagnetic energy comprising a hol#- low conducting member having two perpendicular axes and being non-symmetrical with respect to one of said axes, whereby the electric Vcomponent ofan electromagnetic field resonant therein converges toward one portion of the inner 

